The Baum-Connes conjecture.
The index of projective families of elliptic operators.
The signature package on Witt spaces
In this paper we prove a variety of results about the signature operator on Witt spaces. First, we give a parametrix construction for the signature operator on any compact, oriented, stratified pseudomanifold which satisfies the Witt condition. This construction, which is inductive over the ‘depth’ of the singularity, is then used to show that the signature operator is essentially self-adjoint and has discrete spectrum of finite multiplicity, so that its index—the analytic signature of —is well-defined....
Trace class pseudodifferential calculus with operator valued symbols and unusual index formulas
For several classes of pseudodifferential operators with operator-valued symbol analytic index formulas are found. The common feature is that usual index formulas are not valid for these operators. Applications are given to pseudodifferential operators on singular manifolds.
Travaux de N. Higson et G. Kasparov sur la conjecture de Baum-Connes
Twisted K-theory of differentiable stacks